# TYPES OF SAMPLING IN ANALOG COMMUNICATION Smita R

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TYPES OF SAMPLING IN ANALOG COMMUNICATION Smita R Kadam Department of Electronics and Telecommunication International Institute of Information Technology, I²IT www. isquareit. edu. in 1

• What is Sampling? Sampling is the process of converting continuous time signal into discrete time signal by sensing analog signal value at discrete instants of time To convert this discrete time signal back to continuous time signal without error, there is a condition related to rate at which these samples should be taken and this condition is given by sampling theorem International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 2 Phone - +91 20 22933441/2/3 | Website - www. isquareit. edu. in | Email - [email protected] edu. in

What is need of sampling? • All real life signals are continuous time signals which carries message signal • Digital systems can not process continuous time signals so continuous time signal need to be converted into digital form • Analog to digital conversion sets foundation for modern digital communication systems • Extensive use of Digital technology International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 3 Phone - +91 20 22933441/2/3 | Website - www. isquareit. edu. in | Email - [email protected] edu. in

Process of Sampling S(t) m(t) Sampler International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 4 Phone - +91 20 22933441/2/3 | Website - www. isquareit. edu. in | Email - [email protected] edu. in

Types of sampling 1. Ideal sampling / Impulse sampling/ Instantaneous sampling 2. Natural sampling 3. Flat top sampling International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 5 Phone - +91 20 22933441/2/3 | Website - www. isquareit. edu. in | Email - [email protected] edu. in

Ideal sampling • A message signal m(t) is multiplied with a periodic pulse train c(t), using a switching sampler • Pulse train is given by equation c(t) = • Width of impulse ‘τ’ is very small reaching to zero appearing at ‘Ts’ intervals • Short pulse means less energy per sample • ‘Ts’ is sampling interval • Samples represents modulating signal at the instant of sampling International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 6 Phone - +91 20 22933441/2/3 | Website - www. isquareit. edu. in | Email - [email protected] edu. in

Ideal sampling t - 6 Ts -4 Ts -2 Ts -Ts 0 Ts 2 Ts 4 Ts 6 Ts Message signal, m(t) Periodic Pulse train, c(t) t t Ideally sampled signal , s(t) International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 7 Phone - +91 20 22933441/2/3 | Website - www. isquareit. edu. in | Email - [email protected] edu. in

Limitations of Ideal sampling • Practically not possible to generate pulse train with very small width that tends to Zero (0) • Very small pulse width, so sampled signal has very less energy at every sample, so largely affected by noise interference • Very high noise interference International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 8 Phone - +91 20 22933441/2/3 | Website - www. isquareit. edu. in | Email - [email protected] edu. in

Natural sampling/PAM • Periodic pulse train c(t) is, with finite pulse width and every sample is with sufficient energy, where impulse sampling has almost zero energy • Amplitude of pulses vary in proportion with modulating signal • ‘Ts’ is periodic time of pulse train acting as a periodic switching signal to the modulator • Natural sampling is also referred as natural PAM where top of the pulse follow the shape of modulating signal • Sampling frequency Fs =1/Ts International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 Phone - +91 20 22933441/2/3 | Website - www. isquareit. edu. in | Email - [email protected] edu. in 9

Natural sampling Message signal, m(t) t τ Periodic Pulse train, c(t) -6 Ts -4 Ts -2 T -Ts 0 Ts 2 Ts 4 Ts t Naturally sampled signal , s(t) t International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 10 Phone - +91 20 22933441/2/3 | Website - www. isquareit. edu. in | Email - [email protected] edu. in

Natural sampling Equation • Fourier series of an un modulated pulse train c(t) is given as C(t) = a 0 + a 1 cos + a 2 cos +. . . We have, S(t) = m(t). C(t) S(t) = a 0. m(t)+ a 1 m(t). cos + a 2 m(t). cos +. . . • above equation shows that sampled signal consist of modulating signal m(t) multiplied by a DC term a 0 • And series of DSBSC type components International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 11 Phone - +91 20 22933441/2/3 | Website - www. isquareit. edu. in | Email - [email protected] edu. in

Natural sampling • Modulating signal spectrum is indicated by M(f) and Wm is the highest frequency component • From the spectrum of sampled signal M’(f) , it is obvious that all the modulating signal spectrum is contained in the baseband part of the spectrum • Original baseband signal m(t) and spectrum M(f) lies in almost same band (then why to use natural PAM ? ) • Pulse modulation allows pulses carrying different modulating signals to be interleaved in time, known as time division multiplexed (TDM) signal • To prevent lower edge of the DSBSC spectrum( fs -Wm) from overlapping with low-frequency spectrum (0 - Wm), the separation Δ between these two must not be less than zero International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 12 Phone - +91 20 22933441/2/3 | Website - www. isquareit. edu. in | Email - [email protected] edu. in

Spectrum-Natural sampling M(f) spectrum Aw density a) Spectrum for the modulating signal 0 W Wm M’(f) a 0 Aw a 1 Aw 0 Wm fs -Wm a 2 Aw fs fs +Wm 2 fs-Wm 2 fs +Wm b) Spectrum for the natural PAM wave 3/31/2020 13

Natural sampling • This condition imposed on the sampling frequency states that the sampling frequency must be at least twice the highest frequency in modulating signal- sampling theorem • If sampling condition is not met then, parts of the spectra may overlap and once such overlap is allowed to occur then spectra can not be separated by filtering • High frequency component in DSBSC spectrum (fs -w) appear in the low frequency part of the spectrum, effect is termed as aliasing 14

Aliasing effect - Natural sampling M’(f) a 0 Aw a) Part of the Spectrum for the natural PAM Showing the required separation a 1 Aw 0 Wm fs fs -Wm fs +Wm Δ M’(f) a 0 Aw a 1 Aw 0 3/31/2020 fs -Wm Wm fs b) Spectrum for the natural PAM wave 2 fs-Wm 15

Natural sampling • To avoid aliasing, the modulating signal is first passed through an ant aliasing filter which cuts the signal spectrum off at some value Wm • If the pulse width of the carrier pulse train used in natural sampling is made very short compared to the pulse period , the natural PAM becomes Instantaneous PAM • Short pulse means less energy per sample and magnitudes of the coefficients a 0, a 1… are directly proportional to the pulse width • Therefore to maintain reasonable pulse energy a sample and hold circuit is used in flat top sampling International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 16 Phone - +91 20 22933441/2/3 | Website - www. isquareit. edu. in | Email - [email protected] edu. in

Natural sampling • Due to its wideband nature PAM has very restricted range of applications for direct transmission of signals • Minimum noise interference with sampled signals Applications • In instrumentation systems for computer interfacing • In analog to digital converters (A/D) International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 17 Phone - +91 20 22933441/2/3 | Website - www. isquareit. edu. in | Email - [email protected] edu. in

Flat top sampling • Tops of the samples are flat and constant so these are called Flat top sampling or Practical sampling • Sample and hold circuit is used for flat top sampling • Vm is a message signal • Ct is a periodic pulse train of pulse width ‘τ’ and interval Ts • A periodic train of clocking pulse Ct controls switching of transistor Q 1 18

Sample and Hold circuit • Instantaneous samples from message signal are passed to the capacitor ‘C’ whenever ‘Q 1’ is ON • Each sample is held in the capacitor for time period ‘T’ • A delayed clock pulse c(t) operate the transistor switch Q 2 to discharge the capacitor before the next sample arrives • In this way flat topped samples are formed that provide the input to A/D converter International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 19 Phone - +91 20 22933441/2/3 | Website - www. isquareit. edu. in | Email - [email protected] edu. in

Flat-top sampling Message signal, m(t) τ Periodic Pulse train, c(t) -6 Ts -4 Ts -2 T -Ts 0 Ts 2 Ts 4 Ts Flat top sampled signal, s(t) International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 20 Phone - +91 20 22933441/2/3 | Website - www. isquareit. edu. in | Email - [email protected] edu. in

Flat-top sampling • Frequency spectrum of this flat topped samples M(f) is denoted M(f) = A. M(f) e-jπft. Sinc f. T A is constant Exponential term indicates effect of time delay ‘T’ which does not distort the message signal sinc f. T represents a amplitude distortion which must be corrected • Also called as Pulse amplitude sampling (PAM) • High noise interference • Wide band in nature so restricted range of applications for direct transmission of signal • Used as a intermediate stage in Pulse code modulation • Used in instrumentation system and in analog to digital conversion for computer interfacing International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 21 Phone - +91 20 22933441/2/3 | Website - www. isquareit. edu. in | Email - [email protected] edu. in

Aperture effect • The effect that flat topped samples have on the spectrum is termed as Aperture effect Sinc f. T = • Here, sampling of baseband signal cannot be recovered exactly by passing the samples through an ideal low pass filter • Distortion is due to flat top sampling (not large) • If pulse width ‘τ’ is very small aperture distortion will be small and as τ 0 (instantaneous sampling) distortion approaches ‘ 0’ • This distortion coming from the aperture effect is compensated in the receiver by using equalizer filter • Equalizer filter has reverse characteristics to that of Sinc function • Flat top sampling has the merit that it simplifies the design of the electronic circuitry used to perform sampling operation International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 22 Phone - +91 20 22933441/2/3 | Website - www. isquareit. edu. in | Email - [email protected] edu. in

References • R Taub, D Schilling and G Saha, Principles of Communication Systems, 3 rd edition, Mc Graw Hill, 2012 • D Roddy, J Coolen, Electronic Communication, 4 th edition, Pearson, 2011 • B P Lathi, Zhi Ding, Modern Digital and Analog Communication systems, 4 th edition International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 Phone - +91 20 22933441/2/3 | Website - www. isquareit. edu. in | Email - [email protected] edu. in

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